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Graph Visualization, also known as Graph Drawing, aims to find geometric embeddings of graphs that optimize certain criteria. Stress is a widely used metric; stress is minimized when every pair of nodes is positioned at their shortest path…
In a directed graph $G=(V,E)$ with a capacity on every edge, a \emph{bottleneck path} (or \emph{widest path}) between two vertices is a path maximizing the minimum capacity of edges in the path. For the single-source all-destination version…
Graph Neural Networks (GNNs) excel in various graph learning tasks but face computational challenges when applied to large-scale graphs. A promising solution is to remove non-essential edges to reduce the computational overheads in GNN.…
Vector graphics are widely used in digital art and highly favored by designers due to their scalability and layer-wise properties. However, the process of creating and editing vector graphics requires creativity and design expertise, making…
This paper focuses on automatic guided vehicle (AGV) trajectory planning in the presence of moving obstacles with known but complicated trajectories. In order to achieve good solution precision, optimality and unification, the concerned…
Finding shortest paths in a graph is relevant for numerous problems in computer vision and graphics, including image segmentation, shape matching, or the computation of geodesic distances on discrete surfaces. Traditionally, the concept of…
Hierarchical, multi-resolution volumetric mapping approaches are widely used to represent large and complex environments as they can efficiently capture their occupancy and connectivity information. Yet widely used path planning methods…
This paper aims at constructing a good graph for discovering intrinsic data structures in a semi-supervised learning setting. Firstly, we propose to build a non-negative low-rank and sparse (referred to as NNLRS) graph for the given data…
We investigate graph-based representations of astronomical light curves for transient classification on a quality-controlled, class-balanced subset of the MANTRA benchmark (minimum coverage N_min=100 epochs; N=1705 objects after filtering…
Structured sparse optimization is an important and challenging problem for analyzing high-dimensional data in a variety of applications such as bioinformatics, medical imaging, social networks, and astronomy. Although a number of structured…
The most popular graph indices for vector search use principles from computational geometry to build the graph. Hence, their formal graph navigability guarantees are only valid in Euclidean space. In this work, we show that machine learning…
This paper presents a simple and efficient approach for finding the bridges and failure points in a densely connected network mapped as a graph. The algorithm presented here is a parallel algorithm which works in a distributed environment.…
Image Representation Learning is an important problem in Computer Vision. Traditionally, images were processed as grids, using Convolutional Neural Networks or as a sequence of visual tokens, using Vision Transformers. Recently, Vision…
This study develops a graph search algorithm to find the optimal discrimination path for the binary classification problem. The objective function is defined as the difference of variations between the true positive (TP) and false positive…
Constructing a spanning tree of a graph is one of the most basic tasks in graph theory. We consider this problem in the setting of local algorithms: one wants to quickly determine whether a given edge $e$ is in a specific spanning tree,…
Efficient layout of large-scale graphs remains a challenging problem: the force-directed and dimensionality reduction-based methods suffer from high overhead for graph distance and gradient computation. In this paper, we present a new graph…
Given a graph of which the n vertices form a regular two-dimensional grid, and in which each (possibly weighted and/or directed) edge connects a vertex to one of its eight neighbours, the following can be done in O(scan(n)) I/Os, provided M…
Graph representation of structured data can facilitate the extraction of stereoscopic features, and it has demonstrated excellent ability when working with deep learning systems, the so-called Graph Neural Networks (GNNs). Choosing a…
In a series of papers, Avraham, Filtser, Kaplan, Katz, and Sharir (SoCG'14), Kaplan, Katz, Saban, and Sharir (ESA'23), and Katz, Saban, and Sharir (ESA'24) studied a class of geometric optimization problems -- including reverse shortest…
For two vertices $s$ and $t$ in a graph $G=(V,E)$, the next-to-shortest path is an $st$-path which length is minimum amongst all $st$-paths strictly longer than the shortest path length. In this paper we show that, when the graph is…